Abstract: This paper presents a numerical method based on finite elements in both the frequency and time domains for modeling the coupling of an incident wave with a conducting wire placed inside a metallic cavity having a small aperture. The method uses edge elements on tetrahedra for the electric field representation. The formulation can take into account thin wires as well as lumped elements. In the time-domain approach, the time derivatives are discretized by the Newmark method, which allows obtaining an unconditionally-stable scheme with second-order accuracy. Numerical results are provided to validate the presented method.

Abstract: This paper describes the development of the modified resistance network method (RNM) for analyzing the dynamic behaviors of X-shaped grooves aerostatic bearing with a passive disk-spring compensator. The Newmark integration method and the modified RNM, which takes into account on the equilibrium of the mass flow rate and the squeeze film effect, are used to analyze the time-dependent dynamic behaviors. Results show that after impulse most of the vibrations are absorbed by the disk-spring compensator and the table can maintain a small vibration around the equilibrium position.

Abstract: The Semi-Analytical Finite Element method is an effective method for modeling the load response of structures in which the material properties and problem geometry do not change in one coordinate direction. The method offers considerable savings in computational requirements compared to a full three-dimensional finite element analysis, yet allows the modeling of complex pavement design situations such as those involving cracks or non-homogeneous layers. In this paper, the background to, and theoretical basis of the semi-analytical finite element method is presented. The application of the method to a pavement response evaluation is illustrated. Results obtained with the semi-analytical finite element method are compared with the corresponding theoretical (closed-form) solution. It is shown that there is a good agreement between results obtained with the theoretical solution and those obtained with the semi-analytical finite element method.

Abstract: Recently, a new type of time step integration algorithms using complex time steps has been proposed. For linear problems, the algorithms are higher order accurate, unconditionally stable and have directly controllable numerical dissipation. Solutions with high accuracy can be generated using large time steps. In this paper, the algorithms are extended to solve non-linear problems. The pseudo-force approach is adopted in treating the non-linear terms. To maintain the solutions accuracy, the pseudo-force is reconstructed by interpolation. Special treatments are required to compute the excitation at the complex time steps. Several numerical examples are analysed. It is observed that the complex time step method can be computationally more efficient than the Newmark method when very accurate numerical solutions are required. Copyright © 2002 John Wiley & Sons, Ltd.

Abstract: An explicit Runge-Kutta method is proposed for the numerical integration of special systems of ordinary differential equations. Fifth-order four-stage numerical schemes are constructed taking into account the structural features of the integrated system at the algorithmic level.

Abstract: The finite element method in time domain is a fast and reliable numerical method for predicting the steady state response of the nonlinear dynamic system under periodic excitation. The stability of solutions can be investigated by the application of Floquet-Lyapunov theorem on the transition matrix. Close agreement is found between obtained results and the published findings of a harmonic balance method.

Abstract: Dynamic response of layered pavements subjected to dynamic loads is analyzed by using the three dimensional(3D) finite element method in conjunction with NEWMARK integration scheme.The present results are compared with the available theoretical result to validate the accuracy of the present algorithm. A study is conducted to evaluate the effects of various parameters on the dynamic response of layered pavements subjected to dynamic loads.

Abstract: This paper discusses the dynamic response of airfield pavement subjected to aircraft wheel loading, using the finite element method to determine the response of the system. A 3D finite element program for dynamic analysis in time domain has been developed using Newmark integration scheme for the discretization in time domain. The dynamic response to moving aircraft wheel loads is investigated and the influences of moving load speed, thickness of asphalt layer and wheel configurations on the response are studied. The comparisons of pavement responses were also conducted for static, moving as well as impulsive forces.

Abstract: The dynamic response of the gear is analyzed under impact load by means of DFEM(Dynamic Finite Element Method) in this thesis, using 2 D FEM (Two Dimentional Finite Element Method). Several adjacent teeth under load are discretized by relatively densy grids. The curve of impact load is obtained by means of experimental method. In order to reflect the effect of impact load and impact moving load on whole gear's stress, smaller interval of time is used. The interval of time is 1 μs under impact moving load, and 0.1 μs under impact load. Thus, the results of high accuracy are obtained. As a problem of impacting, it is not suited for using the mode superposition technique because many modes are ensued and the history of response is short. Therefore, the Newmark Method is used in this researching.

Abstract: Through analysis of the coupling problem between structure and ideal liquid, some researches were done on the dynamic responses of solid liquid coupling system using FEM. The precise time integration method, Wilson θ method and Newmark method were used. Some numerical examples were given and the results show that the precise time integration method is in high agreement with the exact solution, not being restricted with the time step, and with a little amount of calculation work. It is adaped to the analysis of dynamic response of solid liquid coupling system.

Abstract: This paper applies a staged method to the dynamic response analysis of liquid-filled tank under earthquake. A finite element model of liquid-filled tank is set up. Taking into account earthquake effect leads to additional load to the coupling equations. A cylindrical liquid-filled tank is studied using the model. It is found that the response of structures to the earthquake loading is much different from that of fluid. The advantage of the staged method is also verified. It is shown that the staged method is more efficient and cost-effective than the whole solution method.

Abstract: A finite element formulation for the time-domain analysis of linear transient elastodynamic problems is presented based on the weak form obtained by applying the Galerkin\'s method to the integro-differential equations which contain the initial conditions implicitly and does not include the inertia terms. The weak form is extended temporally under the assumptions of the constant and linear time variations of field variables, since the time-stepping algorithms such as the Newmark method and the Wilson theta-method are not necessary, obtaining two kinds of implicit finite element equations which are tested for numerical accuracy and convergency. Three classical examples having finite and infinite domains are solved and numerical results are compared with the other analytical and numerical solutions to show the versatility and accuracy of the presented formulation.

Abstract: A space frame structure with consistence mass system having six degrees of freedom (three translations along x, y, z-axes and three rotations about these axes) at each node resting on laminated rubber bearing and subjected EI Centro earthquake ground motion is analysed. A step-by-step Newmark method is adopted to solve the equation of dynamic equilibrium. The response of structure isolated at base is compared with the response of the structure fixed at base. The response of isolated system is found to be less in comparison to the corresponding response without isolation system, implying that the isolation is effective in reducing the response of the structure.

Abstract: In this paper, robotic manipulator links are modeled with finite elements where each element has a uniform cross-section. Shear deformations and rotary iner tia effects are taken into account in this study. Structural damping has also been included in the formulation. The dynamic response of the system has been analyzed b y solving the e igenvalue problem and the modal analysis has been used to describe the behavior of the system. Considering rigid-body, elastic, normal, Coriolis and tangential accelerations result in a nonlinear structural response. Predictorcorrector procedure in connection with the Newmark method is employed for the solution of the resulting matrix d ifferential equation. Robotic manipulator has been considered as a parallelogram linkage. Elastic displacements of end-effector are determined for different l ength of the links. Results of the numerical simulations were compared to tip displacement of the planar two-link manipulator. The e ffect of extension of the output link on the deflection has been investigated for a closedloop p arallelogram m anipulator. The tip d isplacements in the vertical and horizontal directions decrease when the c enter of mass of the output link is moved away fr om the end-effector in both trajectories. The tip d eflections were c ompared to the planar two-link manipulator with the parallelogram mechanism. The tip d eflection produced by closed-chain manipulator is smaller and less fluctuates than those obtained for open-loop manipulator. This characteristic is more pronounced especially for horizontal trajectory.

Abstract: The Finite Element Method (FEM) is a powerful numerical technique that can be used to analyze complex engineering problems. It is particularly useful for problems that include geometric and/or material nonlinearities, as well as situations where underlying differential equations describing physical or biological phenomenon are nonlinear. Since most soil-machine/soil-plant interaction problems involve both material and geometric nonlinearties, FEM has been widely used to analyze soil/machine and soil/plant interaction problems. For example, in a root growth or a tillage problem interface elements are necessary to properly model the soil-root or soil-tillage tool interface. Moreover, soil is an elasto-plastic material that leads to material nonlinearity. A soil-traction device (a tire, for example) interaction problem involves geometric nonlinearity due to the soil-tire interaction (contact problem) and the elasto-plastic behavior of soil as well as the tire material (a layered, composite, incompressible material). Furthermore, these problems include large displacements and strains. The availability of many commercial general purpose software packages such as ANSYS and ABAQUS, which incorporate elasto-plastic behavior of soil and include a large selection of element types including contact and interface elements, makes FEM a particularly attractive technique to analyze soil-machine interaction problems. However, it should be noted that intrinsic to the use of FEM in the context of soil-machine interaction is the assumption that continuum mechanics applies to this case Alternate methods that do not require continuum assumptions, such as the Discrete Element Method (DEM), have been used in soil mechanics with some success. Their primary disadvantage is the requirement of huge computer memory even to solve a very small problem, since equations of motion of each particle within the system and its interaction with its neighbor are continuously accounted. There is a potential to reduce computational costs while still taking advantage of the capabilities of DEM to model fracture by combining FEM and DEM methods (Mujiza et al, 1995). The original formulations of DEM were derived for purely frictional materials and have been applied for analyzing the behavior of sands. Anandarajah (1994) extended the DEM model to include cohesive behavior of soils. Initial research towards simulating the behavior of adhesive and cohesive-frictional agricultural soils in soil-tire and soil-tool interaction problems using DEM were reported by Oida et al. (1999) and Tanaka et al. (1999), respectively.